Remark 5 We compare and contrast the two proofs as follows. The difference operator proof of this section is conceptually simple yet dealing with the contours of integration is rather involved, and indeed we have referenced the original works for the details. The fermionic proof requires the heavy machinery of Fock space, yet the contours fall out naturally from the quasi-commutations (REF ) and (REF ). However, the difference operator proof yields observables in non-determinantal cases as well, and this was indeed the original idea of Borodin and Corwin [1]}. In particular, the equation (REF ) and its ilk are of particular interest in determinantal and non-determinantal cases alike as they are Laplace transforms of the particle positions and through them one can obtain edge asymptotics even in the absence of the full \(n\) -point correlation function. The Fock space proof can be used for orthogonal purposes: investigating the \(\tau \) -function structure of correlation functions [2]}, [3]} and its relations to enumerative geometry, matrix models, and the like. This has indeed been hinted at already by Baker [4]}.

